PRP Records

Probable Primes Top 10000

(277054 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
90016^97783+7776090Lelio R Paula01/2015
9002(5*10^76083-179)/376084Robert Price10/2020
9003(2^252716+1842)/276075Stefano Morozzi01/2020
90042^252712-10576074Lelio R Paula03/2012
9005(10^76069-19)/976069Robert Price10/2017
9008131^35927+276068Lelio R Paula05/2013
9006(41*10^76067+373)/976068Robert Price04/2017
9007(10807^18859-1)/1080676068Serge Batalov08/2020
90092^252683-13976066Lelio R Paula03/2012
9010137^35597-13676061Norbert Schneider05/2015
90113^159413+10676060Lelio R Paula01/2015
9012(2^252593+1682)/276038Stefano Morozzi01/2020
90139^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
9014(6716^19867-1)/671576030Serge Batalov08/2020
901522235^2626+2626^2223576029Hans Havermann12/2019
9016(2^252557-9)/7176026Lelio R Paula07/2012
9018(85*10^76021-103)/976022Robert Price10/2017
9017(2^252539+2690)/276022Stefano Morozzi01/2020
901911^72989+8076011Lelio R Paula02/2015
902099877!6-3675996Robert Price11/2018
90212^252449-45952375995Enzo Doria05/2015
902220^58408+7375991Lelio R Paula01/2015
90232^252418-142175986Yves Minet01/2013
9024(11*2^252396-1)/575980Lelio R Paula02/2014
902520871^4366+4366^2087175973Hans Havermann01/2020
90262^252365-11068975970Enzo Doria05/2014
902711^72949-102075969Enzo Doria11/2012
9028(2^252335+2394)/275961Stefano Morozzi01/2020
9029(2^252294+47)/654975945Lelio R Paula07/2012
9030(166*10^75941-7)/375943Robert Price11/2020
90312^252261-11059575939Enzo Doria05/2014
90327^89853+7675935Lelio R Paula01/2015
9033(3043^21799-1)/304275930Serge Batalov08/2020
90343^159132+5675926Lelio R Paula01/2015
9035730^26513+26513^73075916Norbert Schneider11/2016
90367*10^75911-5775912Robert Price06/2020
9037(27*2^252163-1)/194575907Lelio R Paula01/2014
90385^108596-1484675906Enzo Doria02/2013
9039(1377^24179-1)/137675894Serge Batalov07/2020
9040(2^252082+2734)/275884Stefano Morozzi01/2020
90415^108560-1484675881Enzo Doria02/2013
90422^252051-11035975875Enzo Doria05/2014
90432^251971-11050975851Enzo Doria05/2014
9044(42457^16384+1)/32768275819Lelio R Paula11/2011
90452^251842-471575812Yves Minet05/2019
904699655!6-275811Robert Price07/2017
9047(2^251823+3290)/275806Stefano Morozzi01/2020
904814*10^75798+108975800Jens K. Andersen11/2007
90492^251784-45575795Yves Minet03/2012
90502^251780-128975794Yves Minet01/2013
90512^251760-21560975788Paul Bourdelais03/2013
905221947^2838+2838^2194775784Hans Havermann01/2020
905399^37973+275781Lelio R Paula05/2013
9054(185*10^75777+7)/375779Robert Price02/2017
90555*2^251690+375767Lelio R Paula06/2014
90566^97366+9575766Lelio R Paula01/2015
9057(4742^20611-1)/474175762Serge Batalov08/2020
9058s(23010)75760Hans Havermann11/2017
9059(2^251666+1882)/275759Stefano Morozzi01/2020
90608*6^97337-775744Lelio R Paula10/2014
906124045^1412+1412^2404575738Hans Havermann01/2020
90622^251588-11167775736Enzo Doria05/2014
9063(2^251580+2086)/275733Stefano Morozzi01/2020
90645^108346-1325675731Enzo Doria02/2013
9065(2^251570+1182)/275730Stefano Morozzi01/2020
9066(31^50777+1)/3275726Robert Price07/2013
9067(10^75707+77)/375707Robert Price01/2017
9068(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
90692^251466+19375699Lelio R Paula03/2012
9070(2^251463+1338)/275698Stefano Morozzi01/2020
9071(5*2^251464+1)/942375695Lelio R Paula07/2012
90722^251422-10999175686Enzo Doria04/2014
907391*(10^23+1)*(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)75680Makoto Kamada03/2019
9074(2^251355+3806)/275666Stefano Morozzi01/2020
9075(2^251347+1278)/275663Stefano Morozzi01/2020
90764*5^108245-375661Lelio R Paula10/2014
9077(25*10^75653+143)/375654Robert Price08/2020
9078(2^251261+846)/275637Stefano Morozzi01/2020
9079(2^251195+3770)/275617Stefano Morozzi01/2020
908012^70067-11^7006775615Jean-Louis Charton11/2006
908112^70066+9575614Lelio R Paula02/2015
9082(2^251181+1130)/275613Stefano Morozzi01/2020
9083-E20534/206375607Thomas Ritschel02/2017
908419^59120-5075600Lelio R Paula01/2015
908518^60222-469775596Enzo Doria03/2013
908618^60211-435575582Enzo Doria03/2013
90877*2^251014-975564Lelio R Paula06/2014
90886^97101-2575560Lelio R Paula01/2015
90898^83663-7^8366375556Jean-Louis Charton01/2004
9090(2^250974+3838)/275551Stefano Morozzi01/2020
90913^158331-14075544Lelio R Paula01/2015
9092(12235^18481-1)/1223475539Serge Batalov08/2020
9093(29*10^75532-107)/375533Robert Price08/2020
9096(37^48157-1)/3675519Robert Price03/2012
9094(19*10^75518-43)/375519Robert Price10/2017
90952^250868-422975519Yves Minet08/2018
909710^75516+3146775517Patrick De Geest03/2016
909910^75516-10^2256-175516Serge Batalov01/2011
909810^75516-6659175516Patrick De Geest03/2016
91002^250851-18775514Lelio R Paula03/2012
9101(2^250836+466)/275509Stefano Morozzi01/2020
910222273^2454+2454^2227375503Hans Havermann01/2020
9103(43*10^75498-7)/975499Robert Price12/2014
9104(3^158244-5)/24791675497Lelio R Paula06/2012
91054*5^107971-375470Lelio R Paula10/2014
9106(25*10^75465+71)/375466Robert Price01/2017
9107(2^250690+1222)/275465Stefano Morozzi01/2020
9109(5*2^250681-1)/99975461Lelio R Paula01/2014
9108(2^250674+1354)/275461Stefano Morozzi01/2020
9110(2^250670+1878)/275459Stefano Morozzi01/2020
9111(182*10^75456+1)/375458Robert Price02/2017
9112(2^250669-9)/9889772975451Lelio R Paula07/2012
9113(14583^18121-1)/1458275449Serge Batalov08/2020
911410^75441+1375442Robert Price01/2011
911510^75441-992375441Patrick De Geest05/2013
9116(27*2^250546-1)/645775420Lelio R Paula01/2014
91175*7^89231-675410Lelio R Paula10/2014
91192^250503-1699575409Lelio R Paula05/2013
911811^72411-2875409Lelio R Paula02/2015
91203*5^107860-875392Lelio R Paula10/2014
9121(34*10^75387-403)/975388Robert Price10/2017
91242^250426+2983575386Lelio R Paula05/2013
91228*3^157999-775386Lelio R Paula05/2014
9123(15671^17971-1)/1567075386Serge Batalov08/2020
9125(2^250417+2642)/275383Stefano Morozzi01/2020
9126(88*10^75381-43)/975382Robert Price11/2015
9127(2^250394+2902)/275376Stefano Morozzi01/2020
91282^250382-11175575373Enzo Doria05/2014
91292^250374-279805175371Eric Chen03/2016
9130(22*10^75368-1)/375369Robert Price12/2014
91312^250369-454375369Yves Minet03/2019
913220078^5667+5667^2007875360Hans Havermann02/2020
9133(2^250318+2242)/275353Stefano Morozzi01/2020
9134(21398^17401-1)/2139775349Serge Batalov08/2020
9136(19*10^75338+119)/375339Robert Price02/2017
913521517^3172+3172^2151775339Hans Havermann01/2020
91372^250223-185916775325Enzo Doria03/2016
9138(3^157854-7)/6602528275308Lelio R Paula06/2012
9139(2^250164+1578)/275307Stefano Morozzi01/2020
91403^157831-9875305Lelio R Paula01/2015
9141(46^45281+11^45281)/5775290Serge Batalov12/2016
914292^38335-9175282Norbert Schneider01/2016
9143(2^250026+2398)/275266Stefano Morozzi01/2020
91442^250020+1891575264Lelio R Paula05/2013
91452^250002+819375259Lelio R Paula05/2013
9146(2^249996+1678)/275256Stefano Morozzi01/2020
9147(11*2^249977-7)/1575251Renaud Lifchitz02/2011
9148(2^249968+78557)/6375247Lelio R Paula07/2012
9149(5*10^75244+91)/375245Robert Price11/2016
9150(10489!)^2+Prime(10489)75242Robert Price08/2014
915114^65644+6775237Lelio R Paula01/2015
915268383!4+3275236Robert Price09/2019
9153(2^249928-5)/1185905975229Lelio R Paula06/2012
9154129^35638+275218Lelio R Paula05/2013
91552^249853-11047575214Enzo Doria05/2014
9156(5704^20021-1)/570375199Serge Batalov08/2020
915720574^4517+4517^2057475195Hans Havermann01/2020
9158(11720^18481-1)/1171975194Serge Batalov08/2020
91592^249762+7540975186Enzo Doria04/2016
9160565^27318+27318^56575181Norbert Schneider12/2016
9161(2^249741-7)/68575177Lelio R Paula06/2012
91622^249726-11218175176Enzo Doria06/2014
91632^249721+1171575174Lelio R Paula05/2013
9164(2^249705+654)/275169Stefano Morozzi01/2020
9166(38661^16384+1)/275158Lelio R Paula11/2011
9165(15220^17971-1)/1521975158Serge Batalov08/2020
91672^249658-4735575155Lelio R Paula05/2013
9168155^34311+275153Lelio R Paula05/2013
9169(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
9170(23*2^249602+1)/9375138Lelio R Paula08/2012
91712^249522+841575114Lelio R Paula05/2013
91722^249489-11091175104Enzo Doria05/2014
9173(28*10^75078+131)/375079Robert Price02/2017
9174(206*10^75073-17)/975075Robert Price03/2017
9175(2^249384+3330)/275072Stefano Morozzi01/2020
9176(5947^19891-1)/594675071Serge Batalov08/2020
91772^249368-11057375068Enzo Doria05/2014
9178NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
917919167^8248+8248^1916775065Hans Havermann02/2020
9180(2^249375+78557)/4505612575062Lelio R Paula07/2012
9181(26*10^75055-173)/375056Robert Price10/2017
91832^249272+19375039Lelio R Paula03/2012
918217433^17692-17692^1743375039Norbert Schneider11/2019
918414^65468+4375035Lelio R Paula01/2015
918537^47844+3675030Norbert Schneider05/2014
9186(52*10^75027-7)/975028Robert Price12/2014
918717943^15178+15178^1794375024Hans Havermann02/2020
9188(2^249219+494)/275023Stefano Morozzi01/2020
918920^57653+8975009Lelio R Paula01/2015
9190(2^249084+2682)/274982Stefano Morozzi01/2020
91912^249061-186835374975Enzo Doria04/2016
9192(2^249056+1006)/274974Stefano Morozzi01/2020
91937^88713+2*3^8871374972Mike Oakes07/2010
919418325^12334+12334^1832574970Hans Havermann02/2020
91952*6^96313+574947Lelio R Paula10/2014
9197(8*10^74944+49)/374945Robert Price03/2016
9196(1258^24179-1)/125774945Serge Batalov07/2020
9198300^30247+30247^30074926Norbert Schneider11/2014
91992^248866-17174917Lelio R Paula03/2012
9200(714^26251-1)/71374910Serge Batalov08/2020
92016*5^107168-774908Lelio R Paula10/2014
920211^71926+7874904Lelio R Paula02/2015
92032^248824+186939174904Enzo Doria05/2016
92042^248816+111174902Lelio R Paula01/2011
9205V(388219)74890Serge Batalov03/2015
9206159^34017+15874885Norbert Schneider12/2018
92072*F(358297)-174880Henri Lifchitz12/2009
9208(22*10^74874-31)/974875Robert Price04/2015
920911^71892-7680000074868Enzo Doria01/2013
92109*5^107107-474866Lelio R Paula10/2014
92112^248678-71011174860Paul Bourdelais03/2013
9212(14*10^74858+211)/974859Robert Price11/2017
921313^67194+1274851Lelio R Paula01/2015
9214(7*2^248634+1)/7174846Lelio R Paula08/2012
921511^71867-309074842Enzo Doria12/2012
921668057!4-1674841Robert Price11/2019
92172^248609+26214574839Lelio R Paula05/2013
92183^156852+5074838Lelio R Paula01/2015
921918^59607-1174824Lelio R Paula01/2015
92202^248556-11050774823Enzo Doria05/2014
92217^88531-3674818Lelio R Paula01/2015
9222p(15738)#/2+102474814Robert Price07/2017
9223(2^248505+422)/274808Stefano Morozzi01/2020
9224(2^248507+1938)/274808Stefano Morozzi01/2020
922521137^3454+3454^2113774790Hans Havermann11/2019
92264*3^156740-574785Lelio R Paula05/2014
922717918^14907+14907^1791874779Hans Havermann12/2019
9228(32*10^74773-41)/974774Robert Price05/2015
9229(29*2^248384-1)/1374772Lelio R Paula01/2014
923019401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
92312^248357-1279741374763Enzo Doria03/2016
923242^46057+4174762Lelio R Paula07/2012
9233(2^248339+1686)/274758Stefano Morozzi01/2020
923411^71784-300074756Enzo Doria12/2012
923519^58458+1874754Lelio R Paula01/2015
923612^69265-3574750Lelio R Paula02/2015
9237(2^248291+830)/274743Stefano Morozzi01/2020
923911^71771-4800074742Enzo Doria12/2012
9238(7*10^74741+197)/374742Robert Price07/2017
9240(2^248282-5)/5012974736Lelio R Paula06/2012
92412^248252-11010574732Enzo Doria04/2014
9242(7*10^74729+71)/374730Robert Price03/2016
92433^156614-5074724Lelio R Paula01/2015
9244(7*2^248213+1)/13574719Lelio R Paula07/2012
9245(2^248193+870)/274714Stefano Morozzi01/2020
9246(2^248167+1178)/274706Stefano Morozzi01/2020
9247(2^248173+78557)/76774705Lelio R Paula07/2012
9248(2^248145+3866)/274699Stefano Morozzi01/2020
9249125^35622+12474697Norbert Schneider02/2015
9250(2^248114+994)/274690Stefano Morozzi01/2020


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!